Collapsar Gamma-Ray Bursts: how the luminosity function dictates the duration distribution

Abstract

Jets in long-duration $\gamma$-ray bursts (GRBs) have to drill through the collapsing star in order to break out of it and produce the $\gamma$-ray signal while the central engine is still active. If the breakout time is shorter for more powerful engines, then the jet-collapsar interaction acts as a filter of less luminous jets. We show that the observed broken power-law GRB luminosity function is a natural outcome of this process. For a theoretically motivated breakout time that scales with jet luminosity as $L^{-\chi }$ with $\chi \sim 1/3-1/2$, we show that the shape of the $\gamma$-ray duration distribution can be uniquely determined by the GRB luminosity function and matches the observed one. This analysis has also interesting implications about the supernova-central engine connection. We show that not only successful jets can deposit sufficient energy in the stellar envelope to power the GRB-associated supernovae, but also failed jets may operate in all Type Ib/c supernovae.

6 pages, 3 figures, accepted for publication in MNRAS

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• A lesson from GW170817: most neutron star mergers result in tightly collimated successful GRB jets
• A Common Central Engine for Long Gamma Ray Bursts and Type Ib/c Supernovae?
• Gamma-ray burst jet propagation, development of angular structure, and the luminosity function
• Highly Luminous Supernovae associated with Gamma-Ray Bursts I.: GRB 111209A/SN 2011kl in the Context of Stripped-Envelope and Superluminous Supernovae
• Ready, set, launch: time interval between BNS merger and short GRB jet formation
• Collapsar R-Process Yields Can Reproduce [Eu/Fe] Abundance Scatter in Metal-Poor Stars
• Deciphering the properties of the central engine in GRB collapsars
• Toward an inner connection of SNe Ic, SLSNe Ic, XRF connected SNe, SNe Ic-BL, and GRB connected SNe